Dear Husnir,

Yes, using these internal clustering evaluation methods to choose an optimal algorithm is a good strategy. These methods essentially represent the probability that each cluster represents a unique random distribution. Because they consider only the points and clustered labels, comparisons between clustering algorithms are valid.

Yes, these indices are commonly used to evaluate the clustering quality when statistical units are unlabeled (i.e. you don't know the "true" group assignment). Clearly, clustering is used when units are unlabeled, as happen with many real problems. However, in simulation studies is common to generate samples with known labels, so one can be interested in evaluating how close the partition obtained with a clustering algorithm is close to the "true" partition. Similarly, you can evaluate the performances of your clustering algorithm in presence of a labelled dataset. In these cases, measures like the adjusted Rand Index can also be used.